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Validation Case: 3D Triaxial Displacement Secondary Creep (NAFEMS Test 6(b))

This validation case belongs to solid mechanics. The aim of this test case is to validate the following parameter:

• creep material behavior
• standard and reduced integration elements
• automatic time stepping

The simulation results were compared to the results presented in [NAFEMS]$$^1$$.

Geometry

The geometry consists of a cube with edge length $$l$$ = 0.1 $$m$$.

The coordinates for the points in the cube geometry are as tabulated below:

Analysis Type and Mesh

Tool Type: Code Aster

Analysis Type: Nonlinear static

Mesh and Element Types: The meshes for cases A through D are second-order hexahedral one-element meshes. They were created locally and imported to SimScale. For cases E through H, the standard algorithm was used to generate a second-order tetrahedral mesh.

Find below the standard mesh used for cases E through H:

Simulation Setup

Material:

• Steel (linear elastic)
• Isotropic: $$E$$ = 200 $$GPa$$
• $$\nu$$ = 0.3
• $$\rho$$ = 7870 $$kg/m³$$
• Creep formulation:

Boundary Conditions:

• Constraints:
• Fixed value:
• Face ADEH: $$d_x$$ = 0 $$m$$
• Face ABFE: $$d_y$$ = 0 $$m$$
• Face ABCD: $$d_z$$ = 0 $$m$$
• Displacement in x-direction
• Face BCGF: $$d_x$$ = 0.3 $$mm$$
• Displacement in y-direction
• Face CDHG: $$d_y$$ = 0.2 $$mm$$
• Displacement in z-direction
• Face EFGH: $$d_z$$ =0.1 $$mm$$

For all cases, the following advanced automatic time stepping settings were defined under Simulation control:

• Retiming event: Field change
• Target field component: Internal variable V1 (accumulated unelastic strain)
• Threshold value: 0.00005
• Timestep calculation: Mixed
• Field change target: 0.00004

Result Comparison

The secondary creep movement validation is done by comparing the stress ($$\sigma_{xx}$$) after a creep time of 1000 hours. Below you will find the SimScale and reference results from [NAFEMS]$$^1$$:

The displacement of the geometry can be seen below:

Note